The band alignments of twin-plane superlattices in semiconductor nanowires are systematically investigated on the basis of density functional calculations. Our calculations demonstrate that for nanowires with small diameters the quantum-confinement effect is prominent within wurtzite structure regions and the energy gap in wurtzite-structured nanowires is remarkably larger than that including zinc-blende structure. This results in the straddling band alignment, in which both electrons and holes are confined in zinc-blende structure region. The analysis using a simple tight-binding methods also clarifies that the straddling band alignments can be realized when the diameters of nanowires are less than 4-8 nm, leading to full control of band alignments by varying the nanowire diameter. Our results provide the ability of band-alignment tuning and open new possibilities for band engineering.